# Quadratic Equations

Level of Difficulty: ¤¤

Pre-requisites:
• Factorisation by Inspection
• Solving of linear equations

Quadratic Equations are equations where the highest power of the variable is 2 .
e.g:
x² + 2x + 1 = 0 is a quadratic equation
x² + 1 = 0 is also a quadratic equation
x² + 2x = 0 is also a quadratic equation

In general, a quadratic equation takes the form of ax² + bx + c = 0, where a, b and c are constants. b and c can take the values of zero but a cannot be zero (else it becomes a linear equation - highest power 1)

Null Law:
If a × b = 0, then either a = 0 or b = 0
The null law is important as it forms the basis for solving a quadratic equation by using the method of factorisation.

Solving Quadratic Equations by Factorisation:

Here are 2 videos that show the application of Factorisation to solving Quadratic Equations:

URL: http://www.youtube.com/watch?v=E_A_lKzaZdQ

URL: http://www.youtube.com/watch?v=146fXiHsw48

View the powerpoint slides on solving quadratic equations by Factorisation:

In Summary, to solve a quadratic equation by factorisation,
1. Make one side of the equation equal to zero,
2. Factorise the non-zero side,
3. Apply Null Law,
4. Get value for the unknown.

Application of Quadratic Equations:

You will cover one aspect of the application of quadratic equations - in solving word problems.

View the slides for examples: